Math online problems

Learning Geometry
Mutual geometry software (IGS, or propellant geometry environments, DGEs) are computer programs which figure one to create and then cook geometry tutor free, primarily in glide geometry.

In most IGS, one starts constituent by swing a few points and using them to delineate new objects such as lines, circles or additional points. You can also check geometry answers online.

After whatsoever thinking is through, one can act the points one started with and see how the construction changes. Also get information on geometry problem solver

Free math problem solver

Learn online calculus homework

After all, many professional engineers do not hesitate to admit their ignorance of the subject.
As a student you probably view calculus as another illogical memorization of equations that one needs to pass through school.The best engineers only need the number crunching to confirm what they think the result may be. Also get help with calculus answers solved

Multivariable calculus
A study of limits and continuity in multiple dimensions yields many counter-intuitive results not demonstrated by single-variable functions. More help with calculus problems solved. The multiple integral expands the concept of the integral to functions of many variables.

Understnading logical reasoning

Let us learn Logical reasoning test

Following are samples of logical test questions that are usually asked in entrance examinations, topics like logical puzzles, word problems, series completion, clocks problems, coding decoding all these are included under logical reasoning.

All the nine digits are arranged here so as to form four square numbers 9, 81, 324, 576 how would you put them together so as to form a possible square number and a single largest possible square number?
The lowest square number i can think of containing all the nine digits once and only once is 139854276 which is square of 11826 and the highest square number under the same conditions is 923187456 which is the square of 30384. Also get help with relatively prime
Hope you liked the above post, get more help with How to use a Protractor

Inverse Variation

In an Inverse variation, the values of the two variables change in an opposite manner - as one value increases, the other decreases..

Given two variables x and y, the statements

y varies inversely as x,

y is inversely proportional to x.

all mean that y=kx, for some fixed nonzero real number k. The constant k is called the constant of variation or constant of proportionality.

Simple inverse variation problems consist in find a formula and verify what happen with a quantity when we change the other quantity of the problem.

Direct variation relations have the form y = kx where x and y are variables and k is a non-zero constant. When two variables are related in such a way that the ratio of their values always remains the same, the two variables are said to be in direct variation.

In simpler terms, that means if A is always twice as much as B, then they directly vary.

Above are different types of variations.

CIRCLE SEGMENT

A circle segment is an area of a circle informally defined as an area which is "cut off" from the rest of the circle by a secant or a chord. The circle segment constitutes the part between the secant and an arc, excluding the circle's center.

A closed interval corresponding to a finite portion of an infinite line is known as a Line Segment. Line segments are generally labeled with two letters corresponding to their endpoints, say A and B, and then written AB.

The segment of the circle is the region bounded by a chord and the arc subtended by the chord. Finding the circle segment area is very similar to working with the area of a sector.

Multiplying and Dividing Radicals

Our today’s topic is Multiplying and Dividing radicals.

Radicals involve the use of the radical sign (√). Sometimes these are called surd. The radical sign is generally taken to indicate the principal root of the radicand, although any radicand will have n different nth roots. The term radical is sometimes used loosely to refer to the entire expression consisting of radical sign and radicand. A radical is a symbol for the indicated root of a number, for example a square root or cube root; the term is also synonymous for the root itself.

The expression &NA; = P is called the radical expression, where n is the indicated root index, R is a real number and P is the nth root of number R such that Pⁿ = R.

How to Simplify Radical Expression:

You can simplify radical expression by involving variables and also numbers. When using radical expressions you will be able to break down the number into smaller pieces.

The product of two radicals with same index n can be found by multiplying the radicands and placing the result under the same radical. For example, √9 × √25 = √(9×25) = √225 = 15, which is equal to 3 × 5 = √9 × √25. Similarly, radicals with the same index sign can be divided by placing the quotient of the radicands under the same radical, then taking the appropriate root.

Example problem on Radical Expressions Calculator:-

Solve the radical expression √30

Solution:

Given that √40

√40 written as √4 * 10 = 40

√40 = √4 * 10

= √2² * 10

4 has multiples of 2*2 =4

= √2² √10

= 2 √10

The solution is 2√ 10

ACUTE DEFINITION

An angle is the figure formed by two rays sharing a common end point, called the vertex of the angle. The size of an angle is normally characterized by the smallest positive rotation that maps one of the rays into the other.


There are different types of angles like, acute angle, obtuse angle, Right angle, Straight angle, reflex angle, adjacent angle etc.

An angle whose measure is less than 90° is known as an acute angle. It is also known as a positive angle that measures less than 90°

Acute Definition: The measure of an angle with a measure between 0° and 90° or with less than 90° radians.

To learn about special angle values click here.

PROPERTIES OF MULTIPLICATION

Multiplication (symbol "×") is the mathematical operation of scaling one number by another. It is one of the four basic operations in elementary arithmetic. For example: 2 times 4 is written as 4*2=8
There are four properties of Multiplication which makes multiplication easier and simpler. They are as follows:

Commutative property: When two number are multiplied together, the product is the same regardless of the order of the multiplicands. For example 4 * 2 = 2 * 4
Associative Property: When three or more numbers are multiplied, the product is the same regardless of the grouping of the factors. For example (2 * 3) * 4 = 2 * (3 * 4)

Multiplicative Identity Property of Multiplication: The product of any number and one is that number.

Distributive property: The sum of two numbers times a third number is equal to the sum of each addend times the third number. For example 4 * (6 + 3) = 4*6 + 4*3

Multiplication is often written using the multiplication sign "×" between the terms. It is also denoted by a middle dot or a period.

COMPLEX NUMBERS

Complex numbers are an algebraic way of coding points in the ordinary Euclidean plane so that translation (shift of position) corresponds to the addition of complex numbers and both rescaling (enlargement or shrinking) and rotation correspond to multiplication of complex numbers. ...

DEFINITION OF COMPLEX NUMBERS

Complex Numbers definition: "A complex number is a number comprising a real and imaginary part. It can be written in the form a + bi, where a and b are real numbers, and i is the standard imaginary unit with the property i 2 = −1. ...

Complex numbers are used in a number of fields, including: engineering, electromagnetism, quantum physics, applies mathematics and chaos theory. When the underlying field of numbers for a mathematical construct is the field of complex numbers, the name usually reflects that fact. Complex numbers are plotted on the complex plane, on which the real part is on the horizontal axis, and the imaginary part on the vertical axis.

Two complex numbers are said to be equal if and only if their real parts are equal and their imaginary parts are equal..

Multiplying complex numbers is accomplished in a manner similar to multiplying two binomials. You can use the FOIL process of multiplication, the distributive property, or your personal favorite means of multiplying.

For properties of Complex number click here.

RATIONAL EXPRESSION

A rational expression is an algebraic expression of the form P/Q, where P and Q are simpler expressions (usually polynomials), and the denominator Q is not zero. We can manipulate rational expressions in the same way that we manipulate fractions.

Simplifying Rational Expression Calculator

Thinking back to when you were dealing with whole number fractions one of the first things you did was simplify them: You "cancelled off" factors which were in common between the numerator and denominator. You could do this because dividing any number by itself gives you just "1", and you can ignore factors of "1".To simplify a rational expression, we first factor both the numerator and denominator completely then reduce the expression by cancelling common factors. A rational expression can be simplified or reduced to lowest terms if all common factors from the numerator and denominator are canceled.

Listed in the following picture is one solved example on Simplifying Rational Expressions Calculator:-

Algebraic Method of solving Linear Equations in Two Variables

In the earlier we covered the first method of solving Linear Equations in Two Variables, i.e. the Graphical Method.

Now let move on to the second method of solving Linear Equations in Two Variables, i.e the Algebraic Method.


In a case when the point of intersection of the lines represented by two given equations has coordinates as rational numbers, graphical method is not convenient. This is when we use the a Algebraic method which is a precise method to obtain an accurate answer.

The most commonly used Algebraic Methods of solving Linear Equations in two variables are as follows:

• Method of Elimination by Substitution.
• Method of Elimination by Equating the coefficients.
• Method of Cross Multiplication.

Method of Elimination by Substitution: Elimination by substitution is the method where we express one of the variables in terms of the other variable from either of the two equations and then this expression id put in the other equation to obtain an equation in one variable.

Method of Elimination by Equating the coefficients: In this method, we eliminate one of the two variables to obtain as equation in one variable which can easily be solved.Putting the value of this variable in any one of the given equations, the value of the other variable can be obtained.

Graphical Method of solving Linear Equations in Two Variables

In the earlier posts we discussed about what is a Linear Equation. Further we also understood the meaning of Linear equations in Two variables and listed the various methods to solve the same.

Today let us analyze the first method that is the Graphical Method of Solving Linear Equation in two variables:

Graphical Method: The Procedure of solving a system of Linear Equations in two variables by drawing their graphs is known as Graphical Method.

The following Algorithm can be used to solve a system of Linear Equations in two variables by graphing method:-

Step 1:- Obtain the given system of Simultaneous Linear Equation in x and y.
Let the system of Linear Equation be

A₁ x +b₁ y ₌ c_{1 .....(i)}

A₂ x +b₂ y ₌ c₂ ...(ii)

Step 2:- Draw the graphs of the equations (i) and (ii) in step 1.
Let the lines l₁ and l₂ represent the graphs of (i) and (ii) respectively.

Step 3:- If the lines l₁ and l₂ intersect at a point and (a,b) are the coordinates of this point, then the given system has a unique solution given by x = a,y = b. Otherwise go to step 4.

Step 4:- If the lines l₁ and l₂ are coincident, then the system id consistent and has Infinitely many solutions. In this case, every solution of one of the equations is a solution of the system. Otherwise got to step 5.

Step 5:- If the lines l₁ and l₂ are parallel, then the given system of equations id in consistent i.e.its has no solution.